Question: Express this quotient in scientific notation: ${\frac{2.800\times 10^{-1}} {5.0\times 10^{-5}}}$
Start by collecting like terms together. $= {\frac{2.800} {5.0}} \times{\frac{10^{-1}} {10^{-5}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.56 \times 10^{-1\,-\,-5}$ $= 0.56 \times 10^{4}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.56$ is the same as $5.60 \div 10$ , or $5.60 \times 10^{-1}$ $ = {5.60 \times 10^{-1}} \times 10^{4} $ $= 5.60\times 10^{3}$